Question

8a^3+36a^b+54ab^2+27b^3​

Answer 1

Answer:

8a^3+36a^b+54ab^2+27b^3​= (2a+3b)^3

Hope this helps you! :)

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To simplify:

• $8a^3+36a^2b+54ab^2+27b^3$

Solution:

$8a^3+36a^2b+54ab^2+27b^3 \\\because 8a^3=(2a)^3,\: 36a^2b=3*4a^2*3b=3(2a)^2(3b),\: 54ab^2=3*2a*9b^2=3(2a)(3b)^2,\: 27b^3=(3b)^3 \\ \implies (2a)^3 + 3(2a)^2(3b) + 3(2a)(3b)^2 + (3b)^3 \\\bold{\implies (2a + 3b)^3}$

Formula used:

• $x^3 + 3(x)^2(y) + 3(x)(y)^2 + y^3 = (x+y)^3$

Learn More:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\: (A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\bf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\bf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\bf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\8)\bf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\9)\bf\: A^{3} - B^{3} = (A-B)(A^{2} + AB + B^{2})\\\\ \end{minipage}}$

Hope it helps!!